Question

prove root3 +2 root 5 is irratina

Answer 1

Answer:

Let us assume that 3+2√5 is rational.

Such that there exists two integers a and b such that 3+2√5 = a/b.

2√5 = a/b - 3

2√5 = a - 3b /b

√5 = a - 3b /2b

We know that √5 is irrational.

But it is equal to a-3b/2b where a and n are integers and so it is rational.

But this contradicts the fact that √5 is irrational.

Thus contradiction occurred because of our wrong assumption that 3+2√5 is rational.

HENCE 3+2√5 IS IRRATIONAL.

:)